The invention relates generally to transmission of pulses of energy, and more particularly to the propagation of localized pulses of electromagnetic or acoustic energy over long distances without divergence.
As the Klingon battle cruiser attacks the Starship Enterprise, Captain Kirk commands "Fire photon torpedoes". Two darts or blobs of light speed toward their target to destory the enemy spaceship. Stardate 1989, Star Trek reruns, or 3189, somewhere in intergalactic space. Fantasy or reality. The ability to launch localized packets of light or other energy which do not diverge as they travel great distances through space may incredibly be at hand.
Following the pioneering work of J. N. Brittingham, various groups have been actively pursuing the possibility that solutions to the wave equation can be found that allow the transmission of localized, slowly decaying pulses of energy, variously described as electromagnetic missiles or bullets, Bessel beams, transient beam fields, and splash pulses. These efforts have in common the space-time nature of the solutions being investigated and their potential launching mechanisms, pulse-driven antennas.
Brittingham's original work involved a search, over a period of about 15 years, for packet-like solutions of Maxwell's equations (the equations that describe how electromagnetic waves propagate). The solutions sought were to be continuous and nonsingular (well-behaved, realizable), three-dimensional in pulse structure (localized), and nondispersive for all time (faithfully maintaining their shape). They were also to move at the velocity of light in straight lines and carry finite electromagnetic energy. The solutions discovered, termed focus wave modes (FWMs), had all the aforementioned properties except the last; like plane-wave solutions to the same equations, they were found to have finite energy density but infinite energy, despite all attempts to remove this deficiency, and thus are not physically realizable.
Conventional methods for propagation of energy pulses are based on simple solutions to Maxwell's equations and the wave equation. Spherical or planar waveforms are utilized. Beams of energy will spread as they propagate as a result of diffraction effects. For a source of diameter D and wavelength of .lambda. the distance to which a pulse will propagate without substantial spread is the Rayleigh length D.sup.2 /.lambda..
Present arrays are based on phasing a plurality of elements, all at the same frequency, to tailor the beam using interference effects. In a conventional antenna system, such as a phased array driven with a monochromatic signal, only spatial phasing is possible. The resulting diffraction-limited signal pulse begins to spread and decay when it reaches the Rayleigh length L.sub.R. For an axisymmetric geometry, an array of radius a, and a driving wavelength of .lambda., L.sub.R is about a.sup.2 /.lambda..
There have been several previous attempts to achieve localized transmission beyond this Rayleigh distance with conventional systems. The best known of these are the super-gain or super-directive antennas, where the goal was to produce a field whose amplitude decays as one over the distance from the antenna, but whose angular spread can be as narrow as desired. There are theoretical solutions to this problem, but they turn out to be impractical; the smallest deviation from the exact solution completely ruins the desired characteristics.
The original FWMs can be related to exact solutions of the three-dimensional scalar wave equation in a homogeneous, isotropic medium (one that has the same properties at any distance in all directions). This equation has solutions that describe, for example, the familiar spherical acoustic waves emanating from a sound source in air.
The FWMs are related to solutions that represent Gaussian beams propagating with only local deformation, i.e., a Gaussian-shaped packet that propagates with changes only within the packet. Such a pulse, moving along the z axis, with transverse distance denoted by .rho., ##EQU1## is an exact solution of the scalar wave equation developed by applicant. This fundamental pulse is a Gaussian beam that translates through space-time with only local variations. These pulses can also form components of solutions to Maxwell's equations.
These fundamental Gaussian pulses have a number of interesting characteristics. They appear as either a transverse plane wave or a particle, depending on whether k is small or large. Moreover, for all k they share with plane waves the property of having finite energy density but infinite total energy.
Thus traditional solutions to the wave equation and Maxwell's equations do not provide a means for launching pulses from broadband sources which can travel desirable distances without divergence problems. The laser is a narrowband light source which has a relatively low divergence over certain distances (i.e. relatively long Rayleigh length). However, acoustic and microwave sources, because of longer wavelengths, are more severely limited. Phased arrays do not provide the solution.
Accordingly, it is an object of the invention to provide method and apparatus for launching electromagnetic and acoustic pulses which can travel distances much larger than the Rayleigh length without divergence.
It is also an object of the invention to provide method and apparatus for launching pulses which approximate new solutions to the scalar wave and Maxwell's equations.
It is another object of the invention to physically realize new solutions to the scalar wave and Maxwell's equations which provide localized packets of energy which transverse large distances without divergence.
It is a further object of the invention to provide compact arrays for launching these pulses.